Evangelos Triantaphyllou

Development and evaluation of five fuzzy multiattribute decision-making methods

Abstract We present the development of five fuzzy multiattribute decision-making methods. These methods are based on the analytic hierarchy process (original and ideal mode), the weighted-sum model, the weighted-product model, and the topsis method. Moreover, these methods are examined in terms of two evaluative criteria. Computational results on test problems suggest that although all the methods are inaccurate, some of them seem to be more accurate than the others. The proposed evaluation methodology can easily be used in evaluating more fuzzy multiattribute decision making methods.

An examination of the effectiveness of multi-dimensional decision-making methods: a decision-making paradox

Abstract This paper presents the results of a study that compared four decision-making methods. The methods examined were the weighted sum model, the weighted product model, the analytic hierarchy process, and the revised analytic hierarchy process. Two evaluative criteria were used in an attempt to find the best method. The first criterion was to see if the method when accurate in a multi-dimensional situation remained accurate in a single-dimension case. The second criterion determined the stability of a method in yielding the same outcome when a nonoptimal alternative was replaced with a worse alternative. Tests were conducted using simulated decision problems where random numbers were used for the values of the many combinations of alternatives and criteria. The results illustrate the paradox of deciding on a single best decision-making method. While this paradox is not resolved, useful information is presented for comparing the four methods tested.

Determining the most important criteria in maintenance decision making

Many maintenance decisions require the evaluation of alternative solutions in terms of complex maintenance criteria such as cost, repairability, reliability and availability requirements. Such problems can be formulated as multi‐criteria decision‐making problems. The relative importance of maintenance criteria is difficult to assess, and therefore a sensitivity analysis becomes a necessity. The sensitivity analysis approach presented reveals some counter‐intuitive results and can considerably enhance the application of decision analysis in complex maintenance management.

Multi-Criteria Decision Making Methods

With the continuing proliferation of decision methods and their variants, it is important to have an understanding of their comparative value. Each of the methods uses numeric techniques to help decision makers choose among a discrete set of alternative decisions. This is achieved on the basis of the impact of the alternatives on certain criteria and thereby on the overall utility of the decision maker(s). The difficulty that always occurs when trying to compare decision methods and choose the best one is that a paradox is reached, i.e., What decision-making method should be used to choose the best decision-making method? This problem is examined in Chapter 9.

Fuzzy logic in computer-aided breast cancer diagnosis: analysis of lobulation.

This paper illustrates how a fuzzy logic approach can be used to formalize terms in the American College of Radiology (ACR) Breast Imaging Lexicon. In current practice, radiologists make a relatively subjective determination for many terms from the lexicon related to breast cancer diagnosis. Lobulation and microlobulation of nodules are two important features in the ACR lexicon. We offer an approach for formalizing the distinction of these features and also formalize the description of intermediate cases between lobulated and microlobulated masses. In this paper it is shown that fuzzy logic can be an effective tool in dealing with this kind of problem. The proposed formalization creates a basis for the next three steps (i) extended verification with blinded comparison studies. (ii) the automatic extraction of the related primitives from the image, and (iii) the detection of lobulated and microlobulated masses based on these primitives.

An evaluation of the eigenvalue approach for determining the membership values in fuzzy sets

Abstract The membership values of the elements of a fuzzy set of key importance in any theoretical or practical application of fuzzy set theory. Although there are many methods that evaluate membership values, the methd proposed by Saaty [8,9] based on matrix of pairwise comparisons and eigenvalue theory, is the backbone of many other methods. In this paper we evaluate the above method by using a forward error analysis approach with the assumption that the true membership values in a fuzzy set are continuous in the interval (0, 1). The results reveal that the eigenvalue method is dramatically inaccurate even for fuzzy sets with few members.

Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques

This book will give the reader a perspective into the core theory and practice of data mining and knowledge discovery (DM and KD). Its chapters combine many theoretical foundations for various DM and KD methods, and they present a rich array of examples many of which are drawn from real-life applications. Most of the theoretical developments discussed are accompanied by an extensive empirical analysis, which should give the reader both a deep theoretical and practical insight into the subjects covered. The book presents the combined research experiences of its 40 authors gathered during a long search in gleaning new knowledge from data. The last page of each chapter has a brief biographical statement of its contributors, who are world-renowned experts.

Quantifying data for group technology with weighted fuzzy features

SUMMARY The high potential of using group technology in manufacturing has attracted the interest of both practitioners and researchers. Group technology is based on clustering parts which have similar features. Very often it is very hard to quantify successfully data regarding these features. This is because in many real applications features are fuzzy. This paper identifies two types of fuzzy features: qualitative features, and quantitative ones with subjective meaning. The paper presents a methodology for quantifying the data that refer to the fuzzy features. The proposed methodology deals with crisp and fuzzy data in a unified manner. Finally, some clustering approaches which process the quantified features are also discussed

Interactive learning of monotone Boolean functions

This paper presents some optimal interactive algorithms for some problems related to learning of monotone Boolean functions. These algorithms are based on the fundamental Hansel theorem. The advantage of the algorithms is that they are not heuristics, as is often the case of many known algorithms for general Boolean functions, but they are optimal in the sense of the Shannon function. This paper also formulates a new problem for the joint restoration of two nested monotone Boolean functions f1 and f2. This formulation allows one to further decrease the dialogue with an expert and restore nonmonotone functions of the form f2&|f1. The effectiveness of the proposed approaches is demonstrated by some illustrative computational experiments.

Minimization approach to membership evaluation in fuzzy sets and error analysis

Evaluation of the degree of membership in fuzzy sets is a fundamental topic in fuzzy set theory. Saaty (Ref. 1) proposes a method for solving this problem that has been widely accepted. In this paper, we examine the problem from an error minimization point of view that attempts to reflect the real intentions of the decision maker. When this approach is used, the findings reveal that fuzzy sets of different cardinalities have dramatically different requirements in the consistency level of the input data as far as the error minimization criterion is concerned.